Method of controlling a lithographic apparatus and device manufacturing method, control system for a lithographic apparatus and lithographic apparatus

ABSTRACT

In a method of controlling a lithographic apparatus, historical performance measurements are used to calculate a process model relating to a lithographic process. Current positions of a plurality of alignment marks provided on a current substrate are measured and used to calculate a substrate model relating to a current substrate. Additionally, historical position measurements obtained at the time of processing the prior substrates are used with the historical performance measurements to calculate a model mapping. The model mapping is applied to modify the substrate model. The lithographic apparatus is controlled using the process model and the modified substrate model together. Overlay performance is improved by avoiding over- or under-correction of correlated components of the process model and the substrate model. The model mapping may be a subspace mapping, and dimensionality of the model mapping may be reduced, before it is used.

This application is a continuation of U.S. patent application Ser. No.16/408,605, filed May 10, 2019, now allowed, which is a continuation ofU.S. patent application Ser. No. 15/763,780, filed March 27, 2018, nowU.S. Pat. No. 10,331,040, which is the U.S. national phase entry of PCTPatent Application No. PCT/EP2016/071831, which was filed on Sep. 15,2016, which claims the benefit of priority of European patentapplication no. 15188943.3, which was filed on Oct. 8, 2015, each of theforegoing applications is incorporated herein in its entirety byreference.

FIELD

The present description relates to inspection apparatus and methodsusable, for example, to perform metrology in the manufacture of devicesby lithographic techniques. The description further relates to anillumination system for use in such inspection apparatus and to methodsof manufacturing devices using lithographic techniques. The descriptionyet further relates to computer program products for use in implementingsuch methods.

BACKGROUND

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs). In that instance, a patterning device, whichis alternatively referred to as a mask or a reticle, may be used togenerate a circuit pattern to be formed on an individual layer of theIC. This pattern can be transferred onto a target portion (e.g.,including part of, one, or several dies) on a substrate (e.g., a siliconwafer). Transfer of the pattern is typically via imaging onto a layer ofradiation-sensitive material (resist) provided on the substrate. Ingeneral, a single substrate will contain a network of adjacent targetportions that are successively patterned.

Prior to applying patterns to a wafer using a lithographic apparatus,the wafer generally needs to be measured and modelled so as to properlyalign the wafer and to correct wafer deformations during patterning. Acritical performance measure of the lithographic process is overlay, theaccuracy of alignment of features in two layers in a device (or betweenfeatures formed by two patterning steps in the same layer). Alignmentsensors having multiple color channels are used in the knownlithographic apparatus, to try and obtain the best possible positionmeasurements prior to patterning. These position measurements are usedto calculate a substrate model for each wafer.

To improve overlay, additional measurements are made of performance onprior substrates that have been patterned, to identify and correctdeviations introduced in the patterning step and/or other steps. Varioustools for making such measurements are known, including scanningelectron microscopes, which are used to measure performance parameterssuch as overlay.

SUMMARY

Recently, various forms of scatterometers have been developed for use inthe lithographic field, which allow high volume measurements. Typicallythese measurements made over many prior substrates, provide far greaterspatial detail than can be obtained with alignment measurements made ona current wafer in the course of patterning. Accordingly, types ofmeasurements are used in advanced process control (APC) methods for amodern lithographic production facility. A substrate model based on themeasurements of the current wafer provides wafer-specific corrections,while a process model (or multiple models) provides additionalcorrections to correct for systematic errors in the machine, for examplealignment errors. The cause for these errors often lies in otherprocessing steps, like CMP (chemical and mechanical polishing) andetching, which cause a deformation of the alignment marks. Thisdeformation of the mark results in alignment errors that vary from waferto wafer, when alignment measurements are made in the lithographicapparatus prior to patterning. Because the process model is based onsampling many wafers over time, it can also be provided with (forexample) greater spatial resolution and sensitivity to many othervariables.

Because the process model is designed to implement variations varyingslowly over time, it is not sensitive to wafer-to-wafer variations. Thealignment measurements made on each wafer are sensitive towafer-to-wafer variations. By using a process model in addition to asubstrate model, it has been possible to achieve the high overlayperformance required for modern device manufacture. Nevertheless, thereis a constant quest to improve even further the performance oflithographic processes. This is to improve yield and consistency ofexisting devices, and to allow even smaller devices to be produced infuture.

The inventors have recognized that correlation between the two modelscan result in over- or under-correction of errors in some cases, so thatsome overlay error remains, that is in principle correctable.

The present description describes apparatuses and methods to improveoverlay performance in lithographic processes. One aim is to eliminateor reduce the over- or under-correction of errors that results fromcorrelation between the substrate model and the process model in knownmethods. Another aim is to integrate into one method different types ofcorrections and optimizations that have been implemented in isolation upto now.

According to an aspect, there is provided a method of controlling alithographic apparatus, the method including the steps of:

-   -   (a) obtaining historical performance measurements representing        performance of a lithographic process in applying patterns to a        plurality of prior substrates;    -   (b) using the historical performance measurements to calculate a        process model relating to the lithographic process;    -   (c) after loading a current substrate into a lithographic        apparatus, measuring current positions of a plurality of        alignment marks provided on the current substrate;    -   (d) using the measured current positions to calculate a        substrate model relating to the current substrate; and    -   (e) controlling the lithographic apparatus using the process        model and the substrate model together,    -   wherein the method further comprises:    -   (f) obtaining historical position measurements obtained at the        time of processing the prior substrates;    -   (g) using the historical position measurements and historical        performance measurements together to calculate a model mapping;        and    -   (h) applying the model mapping to modify the substrate model        calculated in step (d) and using the modified substrate model in        step (e).

In an aspect, there is provided a control system for a lithographicapparatus , the control system comprising:

storage for historical performance measurements representing performanceof a lithographic process in applying patterns to a plurality of priorsubstrates;

a process model processor arranged to use the historical performancemeasurements to calculate a process model relating to the lithographicprocess;

a measurement controller for causing to cause measurement of currentpositions of a plurality of alignment marks provided on a currentsubstrate loaded into the lithographic apparatus;

a substrate model processor arranged to use the measured currentpositions to calculate a substrate model relating to the currentsubstrate;

storage for historical position measurements obtained at the time ofprocessing the prior substrates;

a model mapping processor arranged to use the historical positionmeasurements and historical performance measurements together tocalculate a model mapping; and

a patterning controller arranged to control the lithographic apparatususing the process model and the modified substrate model together.

The various storage, controllers and processors of the control systemare identified by their functions in the above summary, and two or moreof these functions may be implemented using common hardware. They may inparticular be implemented by programming one or more processors andcontrollers already present within a lithographic apparatus, an advancedprocess control system and/or a metrology system.

The model mapping is a mathematical mapping between a parameter space ofthe substrate model and a parameter space used by the lithographicapparatus for controlling the patterning. By comparing the historicalperformance data and the historical alignment data, a model mapping canbe established that reduces the problems identified above.

Any parameterized model can be used as the substrate model and theprocess model. In some embodiments, the process model is atwo-dimensional polynomial of, for example, a third or fifth orderpolynomial. In other embodiments, a set of radial basis functions may beused.

In an aspect, there is provided a method of manufacturing deviceswherein product structures are formed on a series of substrates by alithographic process, wherein properties of the product structures onone or more processed substrates are measured by a method as describedherein, and wherein the measured properties are used to adjustparameters of the lithographic process for the processing of furthersubstrates.

In an aspect, there is provided a lithographic apparatus including acontrol system as described herein.

In an aspect, there is provided a computer program product containingone or more sequences of machine-readable instructions for implementingcalculating steps in a method as described herein.

These and other aspects and advantages of the apparatus and methodsdisclosed herein will be appreciated from a consideration of thefollowing description and drawings of exemplary embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of exampleonly, with reference to the accompanying schematic drawings in whichcorresponding reference symbols indicate corresponding parts, and inwhich:

FIG. 1 depicts a lithographic apparatus suitable for use in anembodiment of the present invention;

FIG. 2 depicts a lithographic cell or cluster in which an inspectionapparatus according to an embodiment of the present invention may beused;

FIG. 3 illustrates schematically measurement and exposure processes inthe apparatus of FIG. 1, according to known practice;

FIG. 4 is a schematic diagram of an advanced process control method forcontrolling the apparatus of FIG. 1 according to known practice;

FIG. 5 illustrates the implementation of a substrate model and a processmodel in the method of FIG. 4;

FIG. 6 illustrates the implementation of a modified method with modelmapping in accordance with a first embodiment of the present invention;and

FIG. 7 illustrates the implementation of a modified method with modelmapping in accordance with a second embodiment of the present invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Before describing embodiments of the invention in detail, it isinstructive to present an example environment in which embodiments ofthe present invention may be implemented.

FIG. 1 schematically depicts a lithographic apparatus LA. The apparatusincludes an illumination system (illuminator) IL configured to conditiona radiation beam B (e.g., UV radiation or DUV radiation), a patterningdevice support or support structure (e.g., a mask table) MT constructedto support a patterning device (e.g., a mask) MA and connected to afirst positioner PM configured to accurately position the patterningdevice in accordance with certain parameters; two substrate tables(e.g., a wafer table) WTa and WTb each constructed to hold a substrate(e.g., a resist coated wafer) W and each connected to a secondpositioner PW configured to accurately position the substrate inaccordance with certain parameters; and a projection system (e.g., arefractive projection lens system) PS configured to project a patternimparted to the radiation beam B by patterning device MA onto a targetportion C (e.g., including one or more dies) of the substrate W. Areference frame RF connects the various components, and serves as areference for setting and measuring positions of the patterning deviceand substrate and of features on them.

The illumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic, electrostaticor other types of optical components, or any combination thereof, fordirecting, shaping, or controlling radiation. For example, in anapparatus using extreme ultraviolet (EUV) radiation, reflective opticalcomponents will normally be used.

The patterning device support holds the patterning device in a mannerthat depends on the orientation of the patterning device, the design ofthe lithographic apparatus, and other conditions, such as for examplewhether or not the patterning device is held in a vacuum environment.The patterning device support can use mechanical, vacuum, electrostaticor other clamping techniques to hold the patterning device. Thepatterning device support MT may be a frame or a table, for example,which may be fixed or movable as required. The patterning device supportmay ensure that the patterning device is at a desired position, forexample with respect to the projection system.

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a radiation beamwith a pattern in its cross-section such as to create a pattern in atarget portion of the substrate. It should be noted that the patternimparted to the radiation beam may not exactly correspond to the desiredpattern in the target portion of the substrate, for example if thepattern includes phase-shifting features or so called assist features.Generally, the pattern imparted to the radiation beam will correspond toa particular functional layer in a device being created in the targetportion, such as an integrated circuit.

As here depicted, the apparatus is of a transmissive type (e.g.,employing a transmissive patterning device). Alternatively, theapparatus may be of a reflective type (e.g., employing a programmablemirror array of a type as referred to above, or employing a reflectivemask). Examples of patterning devices include masks, programmable mirrorarrays, and programmable LCD panels. Any use of the terms “reticle” or“mask” herein may be considered synonymous with the more general term“patterning device.” The term “patterning device” can also beinterpreted as referring to a device storing in digital form patterninformation for use in controlling such a programmable patterningdevice.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein may be considered as synonymous with the moregeneral term “projection system”.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g., water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the mask and the projection system. Immersion techniques arewell known in the art for increasing the numerical aperture ofprojection systems.

In operation, the illuminator IL receives a radiation beam from aradiation source SO. The source and the lithographic apparatus may beseparate entities, for example when the source is an excimer laser. Insuch cases, the source is not considered to form part of thelithographic apparatus and the radiation beam is passed from the sourceSO to the illuminator IL with the aid of a beam delivery system BDincluding, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thelithographic apparatus, for example when the source is a mercury lamp.The source SO and the illuminator IL, together with the beam deliverysystem BD if required, may be referred to as a radiation system.

The illuminator IL may for example include an adjuster AD for adjustingthe angular intensity distribution of the radiation beam, an integratorIN and a condenser CO. The illuminator may be used to condition theradiation beam, to have a desired uniformity and intensity distributionin its cross section.

The radiation beam B is incident on the patterning device MA, which isheld on the patterning device support MT, and is patterned by thepatterning device. Having traversed the patterning device (e.g., mask)MA, the radiation beam B passes through the projection system PS, whichfocuses the beam onto a target portion C of the substrate W. With theaid of the second positioner PW and position sensor IF (e.g., aninterferometric device, linear encoder, 2-D encoder or capacitivesensor), the substrate table WTa or WTb can be moved accurately, e.g.,so as to position different target portions C in the path of theradiation beam B. Similarly, the first positioner PM and anotherposition sensor (which is not explicitly depicted in FIG. 1) can be usedto accurately position the patterning device (e.g., mask) MA withrespect to the path of the radiation beam B, e.g., after mechanicalretrieval from a mask library, or during a scan.

Patterning device (e.g., mask) MA and substrate W may be aligned usingmask alignment marks M1, M2 and substrate alignment marks P1, P2.Although the substrate alignment marks as illustrated occupy dedicatedtarget portions, they may be located in spaces between target portions(these are known as scribe-lane alignment marks). Similarly, insituations in which more than one die is provided on the patterningdevice (e.g., mask) MA, the mask alignment marks may be located betweenthe dies. Small alignment mark may also be included within dies, inamongst the device features, in which case it is desirable that themarkers be as small as possible and not require any different imaging orprocess conditions than adjacent features. The alignment system, whichdetects the alignment markers, is described further below.

The depicted apparatus could be used in a variety of modes. In a scanmode, the patterning device support (e.g., mask table) MT and thesubstrate table WT are scanned synchronously while a pattern imparted tothe radiation beam is projected onto a target portion C (i.e., a singledynamic exposure). The speed and direction of the substrate table WTrelative to the patterning device support (e.g., mask table) MT may bedetermined by the (de-)magnification and image reversal characteristicsof the projection system PS. In scan mode, the maximum size of theexposure field limits the width (in the non-scanning direction) of thetarget portion in a single dynamic exposure, whereas the length of thescanning motion determines the height (in the scanning direction) of thetarget portion. Other types of lithographic apparatus and modes ofoperation are possible, as is well-known in the art. For example, a stepmode is known. In so-called “maskless” lithography, a programmablepatterning device is held stationary but with a changing pattern, andthe substrate table WT is moved or scanned.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

Lithographic apparatus LA is of a so-called dual stage type which hastwo substrate tables WTa, WTb and two stations—an exposure station EXPand a measurement station MEA—between which the substrate tables can beexchanged. While one substrate on one substrate table is being exposedat the exposure station, another substrate can be loaded onto the othersubstrate table at the measurement station and various preparatory stepscarried out. This enables a substantial increase in the throughput ofthe apparatus. The preparatory steps may include mapping the surfaceheight contours of the substrate using a level sensor LS and measuringthe position of alignment markers on the substrate using an alignmentsensor AS. If the position sensor IF is not capable of measuring theposition of the substrate table while it is at the measurement stationas well as at the exposure station, a second position sensor may beprovided to enable the positions of the substrate table to be tracked atboth stations, relative to reference frame RF. Other arrangements areknown and usable instead of the dual-stage arrangement shown. Forexample, other lithographic apparatuses are known in which a substratetable and a measurement table are provided. These are docked togetherwhen performing preparatory measurements, and then undocked while thesubstrate table undergoes exposure.

As shown in FIG. 2, the lithographic apparatus LA forms part of alithographic cell LC, also sometimes referred to a lithocell or cluster,which also includes apparatus to perform pre- and post-exposureprocesses on a substrate. Conventionally these include spin coaters SCto deposit resist layers, developers DE to develop exposed resist, chillplates CH and bake plates BK. A substrate handler, or robot, RO picks upsubstrates from input/output ports I/O1, I/O2, moves them between thedifferent process apparatus and delivers then to the loading bay LB ofthe lithographic apparatus. These devices, which are often collectivelyreferred to as the track, are under the control of a track control unitTCU which is itself controlled by the supervisory control system SCS,which also controls the lithographic apparatus via lithography controlunit LACU. Thus, the different apparatus can be operated to maximizethroughput and processing efficiency.

In order that the substrates that are exposed by the lithographicapparatus are exposed correctly and consistently, it is desirable toinspect exposed substrates to measure properties such as overlay errorsbetween subsequent layers, line thicknesses, critical dimensions (CD),etc. Accordingly a manufacturing facility in which lithocell LC islocated also includes metrology system MET which receives some or all ofthe substrates W that have been processed in the lithocell. Metrologyresults are provided directly or indirectly to the supervisory controlsystem SCS. If errors are detected, adjustments may be made to exposuresof subsequent substrates.

Within metrology system MET, an inspection apparatus is used todetermine the properties of the substrates, and in particular, how theproperties of different substrates or different layers of the samesubstrate vary from layer to layer. The inspection apparatus may beintegrated into the lithographic apparatus LA or the lithocell LC or maybe a stand-alone device. To enable most rapid measurements, it may bedesirable that the inspection apparatus measure properties in theexposed resist layer immediately after the exposure. However, not allinspection apparatus have sufficient sensitivity to make usefulmeasurements of the latent image. Therefore measurements may be takenafter the post-exposure bake step (PEB) which is customarily the firststep carried out on exposed substrates and increases the contrastbetween exposed and unexposed parts of the resist. At this stage, theimage in the resist may be referred to as semi-latent. It is alsopossible to make measurements of the developed resist image—at whichpoint either the exposed or unexposed parts of the resist have beenremoved Also, already exposed substrates may be stripped and reworked toimprove yield, or discarded, thereby avoiding performing furtherprocessing on substrates that are known to be faulty. In a case whereonly some target portions of a substrate are faulty, further exposurescan be performed only on those target portions which are good.

The metrology step with metrology system MET can also be done after theresist pattern has been etched into a product layer. The latterpossibility limits the possibilities for rework of faulty substrates butmay provide additional information about the performance of themanufacturing process as a whole.

Alignment Process Background

FIG. 3 illustrates the steps to expose target portions (e.g. dies) on asubstrate W in the dual stage apparatus of FIG. 1. The process accordingto conventional practice will be described first.

On the left hand side within a dotted box are steps performed atmeasurement station MEA, while the right hand side shows steps performedat exposure station EXP. From time to time, one of the substrate tablesWTa, WTb will be at the exposure station, while the other is at themeasurement station, as described above. For the purposes of thisdescription, it is assumed that a substrate W has already been loadedinto the exposure station. At step 200, a new substrate W is loaded tothe apparatus by a mechanism not shown. These two substrates areprocessed in parallel in order to increase the throughput of thelithographic apparatus.

Referring initially to the newly-loaded substrate W, this may be apreviously unprocessed substrate, prepared with a new photo resist forfirst time exposure in the apparatus. In general, however, thelithography process described will be merely one step in a series ofexposure and processing steps, so that substrate W′ has been throughthis apparatus and/or other lithography apparatuses, several timesalready, and may have subsequent processes to undergo as well.Particularly for the problem of improving overlay performance, the taskis to ensure that new patterns are applied in exactly the correctposition on a substrate that has already been subjected to one or morecycles of patterning and processing. Each patterning step can introducepositional deviations in the applied pattern, while subsequentprocessing steps progressively introduce distortions in the substrateand/or the pattern applied to it, that must be measured and correctedfor, to achieve satisfactory overlay performance.

The previous and/or subsequent patterning step may be performed in otherlithography apparatuses, as just mentioned, and may even be performed indifferent types of lithography apparatus. For example, some layers inthe device manufacturing process which are very demanding in parameterssuch as resolution and overlay may be performed in a more advancedlithography tool than other layers that are less demanding. Thereforesome layers may be exposed in an immersion type lithography tool, whileothers are exposed in a ‘dry’ tool. Some layers may be exposed in a toolworking at DUV wavelengths, while others are exposed using EUVwavelength radiation. Some layers may be patterned by steps that arealternative or supplementary to exposure in the illustrated lithographicapparatus. Such alternative and supplementary techniques include forexample imprint lithography, self-aligned multiple patterning anddirected self-assembly.

At 202, alignment measurements using the substrate marks P1 etc. andimage sensors (not shown) are used to measure and record alignment ofthe substrate relative to substrate table WTa/WTb. In addition, severalalignment marks across the substrate W will be measured using alignmentsensor AS. These measurements are used in one embodiment to establish asubstrate model (sometimes referred to as the “wafer grid”), which mapsvery accurately the distribution of marks across the substrate,including any distortion relative to a nominal rectangular grid.

At step 204, a map of wafer height (Z) against X-Y position is measuredalso using the level sensor LS. Primarily, the height map is used onlyto achieve accurate focusing of the exposed pattern. It may be used forother purposes in addition.

When substrate W was loaded, recipe data 206 were received, defining theexposures to be performed, and also properties of the wafer and thepatterns previously made and to be made upon it. To these recipe dataare added the measurements of wafer position, wafer grid and height mapthat were made at 202, 204, so that a complete set of recipe andmeasurement data 208 can be passed to the exposure station EXP. Themeasurements of alignment data for example comprise X and Y positions ofalignment targets formed in a fixed or nominally fixed relationship tothe product patterns that are the product of the lithographic process.These alignment data, taken just before exposure, are used to generatean alignment model with parameters that fit the model to the data. Theseparameters and the alignment model will be used during the exposureoperation to correct positions of patterns applied in the currentlithographic step. The model in use interpolates positional deviationsbetween the measured positions. A conventional alignment model mightcomprise four, five or six parameters, together defining translation,rotation and scaling of the ‘ideal’ grid, in different dimensions. Asdescribed further in U.S. patent application publication no. US2013-230797, advanced models are known that use more parameters.

At 210, wafers W and W are swapped, so that the measured substrate Wbecomes the substrate W entering the exposure station EXP. In theexample apparatus of FIG. 1, this swapping is performed by exchangingthe supports WTa and WTb within the apparatus, so that the substrates W,W′ remain accurately clamped and positioned on those supports, topreserve relative alignment between the substrate tables and substratesthemselves. Accordingly, once the tables have been swapped, determiningthe relative position between projection system PS and substrate tableWTb (formerly WTa) is all that is necessary to make use of themeasurement information 202, 204 for the substrate W (formerly W) incontrol of the exposure steps. At step 212, reticle alignment isperformed using the mask alignment marks M1, M2. In steps 214, 216, 218,scanning motions and radiation pulses are applied at successive targetlocations across the substrate W, in order to complete the exposure of anumber of patterns.

By using the alignment data and height map obtained at the measuringstation in the performance of the exposure steps, these patterns areaccurately aligned with respect to the desired locations, and, inparticular, with respect to features previously laid down on the samesubstrate. The exposed substrate, now labeled W′ is unloaded from theapparatus at step 220, to undergo etching or other processes, inaccordance with the exposed pattern.

Advanced Process Control using Historical Performance Data

For best performance, historical performance data relating to thelithography process are generally used in addition to measurements madewhen a current substrate is loaded into the lithographic apparatus. Forthis purpose, measurements of performance are made with the metrologysystem MET (FIG. 2). Different forms of advanced process control can beimplemented. FIG. 4 illustrates only one example, implementing a knownstability control method.

FIG. 4 depicts a stability module 300. This module is for example anapplication running on a processor, for example within the control unitLACU or the supervisory control system SCS of FIG. 2. Shown are threemain process control loops, labeled 1, 2, 3. The first loop provideslocal control of the lithography apparatus using the stability module300 and monitor wafers. A monitor wafer 302 is shown being passed from alithography cell 304, which may be the lithocell LC of FIG. 2 forexample. Monitor wafer 304 has been exposed with a calibration patternto set ‘baseline’ parameters for focus and overlay. At a later time, ametrology tool 306 reads these baseline parameters, which are theninterpreted by the stability module 300 so as to calculate stabilitycorrections 308 specific to this lithocell. This performance data can befed back to the lithography cell 304, and used when performing furtherexposures. The exposure of the monitor wafer may involve printing apattern of marks on top of reference marks. By measuring overlay errorbetween the top and bottom marks, deviations in performance of thelithographic apparatus can be measured, even when the wafers have beenremoved from the apparatus and placed in a metrology tool.

The second (APC) control loop is based on measurements of performanceparameters such as focus, dose, and overlay on actual product wafers. Anexposed product wafer 320 is passed to metrology tool 322, which may bethe same or different to the metrology tool 306 in the first controlloop. At 322 information relating for example to parameters such ascritical dimension, sidewall angles and overlay is determined and passedto an Advanced Process Control (APC) module 324. This data is alsopassed to the stability module 300. Process corrections 326 arecalculated and used by the supervisory control system (SCS) 328,providing control of the lithocell 304, in communication with thestability module 300.

The third control loop is to allow metrology integration into the second(APC) control loop, for example in double patterning applications. Anetched wafer 330 is passed to metrology unit 332 which again may be thesame or different to the metrology tool 306, 322 used in the firstand/or second control loop. Metrology tool 332 measures performanceparameters such as critical dimensions, sidewall angles and overlay,read from the wafer. These parameters are passed to the Advanced ProcessControl (APC) module 324. The loop continues the same as with the secondloop.

Substrate Model Mapping—Background

For overlay performance, new patterns should be positioned correctlyrelative to patterns already on the substrate, not merely positioned atsome nominally ‘correct’ position. From the above description, it willbe understood that several different mechanisms are implemented toachieve high performance in parameters such as overlay.

FIG. 5 summarizes these mechanisms, as they relate to a patterningoperation on a current substrate, in the known method of controlling thelithographic apparatus LA. At 402 positional deviations of a currentsubstrate are measured by the lithographic apparatus using its alignmentsensors AS, in the manner described with reference to FIG. 3. At 404 asubstrate model SM is calculated from the position measurements of thecurrent substrate that allows substrate-specific corrections to beapplied by the lithographic apparatus at 408 when a pattern is applied.

In addition, at 412 measurements of performance on prior substrates arestored to provide historical performance data. This historicalperformance data is used at 414 to calculate one or more process modelsPM representing the performance of the particular lithographic apparatusand other processing equipment relevant to the current substrate. Thesecalculations may for example the ones done in the control loops of theexample of FIG. 4.

At 416 the substrate model and the process model(s) are combined tocreate a complete substrate and process correction model PSM. Using thecombined model, lithographic apparatus 408 calculates corrections sothat a new pattern can be applied to each substrate, correcting not onlyfor positional deviations in the features already on the substrate, butalso for deviations in performance of the patterning and otherprocessing steps.

Ideally, the substrate model would correct only those deviations thatare not corrected by the process model, and vice versa. The inventorshave recognized that in the known system, an element of correlation canarise between alignment deviations corrected via a substrate model andoverlay errors corrected via a process model. Such correlation canresult in over-correction or under-correction of errors. According tothe present disclosure, by identifying and eliminating thesecorrelations, the performance of the lithographic process as a whole canbe further improved, particularly in terms of overlay.

While a process model PM and a substrate model SM may be referred to inthe singular, the skilled reader will understand that either or both ofthese models may be a superposition of two of more sub-models. Theprocess model may comprise sub-models for performance of thelithographic apparatus and performance of the other processing steps,but all models based on the historical performance data are simplyregarded to as the process model, for simplicity in the presentdisclosure. As a common example, the process model may comprise aninter-field model and an intra-field model. The inter-field modelrepresents variations in performance that are related to position overthe substrate, while the intra-field model represents variations thattend to repeat in each target portion (field) of the substrate. Each ofthese can be further sub-divided into sub-models. Either or both ofthese models may comprise a sub-model specific to a particular productdesign and a sub-model common to a number of product designs. Additionalmodels can apply corrections for transient effects, such as heating ofthe lens, the reticle and/or the substrate. The stability module createsanother sub-model, representing day-to-day drift of actual performancefrom a process model based on historical performance measurements.

Similarly, the substrate model may in practice comprise a combination oftwo or more sub-models. Commonly for example, a four-parameter (4PAR)model will be fitted first. A second model with higher order variationsis then fitted on the residuals of the 4PAR model. (The residualsinclude positional deviations not modeled by the 4PAR model.) The higherorder model may be for example a six-parameter (6PAR) model, a 3^(rd)order polynomial model, or a model based on radial basis functions. Theterm ‘substrate model’ therefore encompasses combination of two or moresub-models. Furthermore, as with the process model, the substrate modelcan comprise an intra-field model as well as inter-field model. In oneexample, multiple alignment marks are measured for a small number offields on the current substrate, and are used to fit an intra-fieldsubstrate model. In that case, the substrate model is effectively acombination of three sub-models: a 4PAR substrate model, higher orderinter-field substrate model and an intra-field substrate model. Eachsuccessive model represents smaller and smaller deviations, but each onehelps to reduce overlay another small amount, which is critical inmodern semiconductor manufacturing.

FIG. 6 shows a modified method of controlling the lithographicapparatus, implementing substrate model mapping to address the problemscaused by correlation between the substrate model and the process modelin the known processes. Steps 502 to 516 correspond to the like-numberedsteps 402 to 416 in the known method of FIG. 5. Some additional stepsand details will be described, which are for implementing the substratemodel mapping. The substrate model mapping will be described firstly inoverview. Further below, a mathematical basis and more detail of anexample implementation will be provided.

Compared with the method of FIG. 5, the principal change in the methodof FIG. 6 is that at step 520 a substrate model mapping is applied tothe substrate model SM, before it is combined with the process model PMat step 516. The applied mapping is defined in one example by a mappingmatrix M. Within step 514 the mapping to be applied is calculated, aswell as the process model PM. To do this, step 514 receives not onlyhistorical performance data 512, but also corresponding historicalposition measurements stored at 522. These comprise the alignmentmeasurements that were obtained by the (same or another) lithographicapparatus, at the time when the prior substrates were patterned. Theyare used in combination with the historical performance data, toidentify and suppress correlations of the type described above. Inaddition to the historical position measurements, associated historiccorrections 524 are stored and used in step 514. Specifically, at 526the corrections that were applied during patterning of each priorsubstrate are effectively undone (for example, subtracted from thehistorical performance data), to recreate the actual positionaldeviations that were present on the prior substrates before usingcorrections. These actual positional deviations (as best they can beknown from the measurements taken before and after the prior patterning)represent the optimal corrections that could have been applied at thetime of patterning each prior substrate.

As an alternative to storing actual corrections at step 524, what couldbe stored is a definition of the models and corrections that wereapplied in the processing of the prior substrate. Given the historicalposition data and the historical performance data relating to a givenprior substrate, the corrections that would have been applied can berecreated. At step 530, the actual positional deviation and the measuredpositional data for each prior substrate are compared to identify thecorrelations mentioned above. The identified correlations are used todefine the process model and the substrate model mapping applied at 520.The substrate model after the mapping has been applied is labeled SM′.

The substrate model mapping may be expressed for example in the form ofa matrix M, as described further below. The substrate model mapping maybe a linear projection, or a nonlinear projection. Generally speaking,each model SM, PM will be expressed in a multidimensional space definedby a respective set of parameters. The set of parameters may be firstorder transformation parameters, such as a the well-known 6PAR modeldefining simple rotations and magnifications. The set of parameters maybe for a higher order model, such as a third order or fifth orderpolynomial model. The polynomials may be in Cartesian coordinates X andY, or they may be in coordinates providing rotational symmetry modes,such as Zernike polynomials. In some embodiments, the model mapping maybe a mapping from a multidimensional space occupied by the substratemodel to a different multidimensional space occupied by the processmodel.

The model mapping may be a subspace mapping. The number of degrees offreedom in the substrate model may be different from the number ofdegrees of freedom in the process model. Typically, the number ofmeasurements made on every current substrate at step 402 or 502 is farlower than the number of measurements that can be made on a fewsubstrates in the off-line metrology tools 306, 322, 332. Therefore finespatial detail will typically be concentrated in the inter-field andintra-field process model, while the substrate model SM describesbroader deviations. In a modern example process, the substrate model maybe for example a third order polynomial model. A third order polynomialin spatial dimensions X and Y may have twenty or so parameters, eachrepresenting a different degree of freedom. (Within this model there areactually two 10-parameter models: one for deviations in the X direction,and one for deviations in the Y direction. With another model deviationsin both directions may be represented together.) The process model PMmay be for example a fifth order model, having 42 parameters andconsequently a greater number of degrees of freedom than the substratemodel. The combined substrate and process model PSM will have a similarnumber of degrees of freedom. In some examples, the parameters of theprocess model are a superset of the parameters of the substrate model,so that the combination at step 416 is a simple addition. In othercases, some transformation between multidimensional spaces may need tobe performed before the addition. This is a detail of implementation. Ineither case, the substrate model mapping at step 520 can exploit theseadditional degrees of freedom to reduce the effects of correlation,mentioned above.

After the model mapping, the dimensions of the substrate model SM′ arenot increased in number, and they may even be reduced. However (in theexample of a linear mapping) they are expressed now in terms of basevectors in the higher-dimensional parameter space of the combinedsubstrate and process model PSM, and not constrained to the degrees offreedom of the original substrate model. As mentioned, nonlinear mappingcan also be envisaged, and linear mappings are used only as an example.The case where the process model has more degrees of freedom than thesubstrate model is only a typical situation, and not a requirement forbenefiting from the model mapping method disclosed herein.

The dimensionality of the subspace mapping may be further reduced,before it is used in step 520. As explained below, this can be useful toeliminate insignificant components, or components that might amplify theeffect of changes in the process in the finished model. As explainedfurther below, the dimensionality may be reduced by performing asingular value decomposition (SVD) of a model mapping matrix andmodifying certain components in a scaling matrix of the singular valuedecomposition. SVD is only one example of a suitable method, and othermethods may be used, such as principal component analysis, canonicalvariate analysis (CVA), also called canonical correlation analysis (CCA)or a discrete empirical interpolation method (DEIM).

Substrate Model Mapping—Mathematical Basis & Implementation

To explain the theory and implementation of the technique describedabove, some definitions and notations are set out. For convenience andfamiliarity with semiconductor processing, wafers will be referred to asan example of substrates. The substrate model SM can be referred to asthe wafer alignment model. The methods disclosed herein may be appliedto other types of substrates, not only semiconductor wafers.

Assume a matrix X to be the wafer alignment model parameters obtainedfrom alignment sensor measurements on multiple wafers. These parametersmay be for example twenty coefficients for a third order polynomialmodel. The dimensions of the matrix are thus the number of wafers timesthe number of parameters in the wafer alignment model(X=[n_(wafers)×n_(params)]). Note that the model can be defined torepresent deviation from an ideal grid, or designed to represent fullythe absolute position of points on the wafer. Both can be the case, fordifferent sub-models. In one example, let the model contain the fullabsolute position (nominal position plus position deviation) but thenominal position is captured in a 4PAR model. The higher-order models(polynomial or radial basis function, for example) are then onlyrepresenting the residual. This is just a choice of implementation.Define OVL to be the parameters (for example fifth order polynomialcoefficients) corresponding to the overlay measurement results(historical performance data) for the same wafers. For simplicity ofargument, assume that the wafer alignment model parameters are a subset(or subspace) of the overlay model parameters, so that simple operationscan be performed like adding/subtracting on them. (If they are not, theywould need to be transformed before being added/subtracted.)

In the lithographic apparatus step 408/508, corrections are derived fromthe models described above. Then denote the wafer alignment correctionsas C_(wa), which are the expose corrections derived for each wafer fromthe wafer alignment model (substrate model SM in FIGS. 4 and 5). Thendenote the process corrections (calculated for example by the APCcontrol loops of FIG. 4) as C_(apc). Note that all these are matricesdescribing parameters of multiple wafers, just like X. From theseparameters the best estimation of the optimal correction Y can bederived as:

Y=C _(wa) +C _(apc) −OVL   (1)

As explained already with reference to FIG. 6, the optimal correction iswhat should (with hindsight based on the historical performance data)have been corrected during patterning (exposure), to obtain perfectoverlay. Note that, although multiple wafers are represented in thesematrices, this equation calculates the “best” corrections on a singlewafer basis. Each column of the matrix X represents a differentparameter and each row of the matrix represents a different wafer:X=[n_(wafers)×n_(params)] The minus-sign before OVL comes from the factthat during overlay measurement, what is measured is positions offeatures in a second layer minus positions of features in a first layer.Wafer alignment is based on measurements of the first layer only, beforethe pattern is applied. Note that it is impossible to use these “optimalcorrections” Y in the patterning step, as the exposure is done beforethe OVL error can be measured. However, as seen in the APC control loopsin the method of FIG. 4, overlay and alignment data from priorsubstrates, can be used to correct operations on a current substrate andon one or more future substrates.

The known APC control loop aims to calculate optimal corrections basedon alignment and overlay data from the prior wafers, trying toapproximate the “true wafer deformation” Y as well as possible, by thecombination of substrate corrections based on measured deformation ofthe current wafer (substrate model SM) plus process corrections obtainedfrom historical data, using the APC control loops (process model PM):

Y≅X+C_(apc)   (2)

The process corrections in the APC control loops are currently updatedby means of an inline calibration, which in a simplified way can bewritten as:

C _(apc−new) =Y−X=C _(apc) −OVL−X,   (3)

where X denotes the mean of X over multiple wafers, C is the newlycalibrated process corrections for future wafers and C _(app) are theactual applied process corrections on the past wafers.

Now, the modified method illustrated in FIG. 6 consists of replacing theapproximation method for the known process correction (equation (2)) bya new equation:

Y≅XM+C_(apc)   (4)

Equation (4) involves matrix multiplication as well as APC processcorrections. Matrix M can be considered as a model mapping matrix,defining a mapping from the wafer alignment model parameter space (X) tothe overlay model parameter space (Y). By adding this model mapping step(step 520), the modified control method has the potential to improveoverlay still further than the current method from equation (2).Calibrations calculations in the control loops can be modified tocalculate not only the process corrections C_(app), but also the modelmapping matrix M. If it is desired to use nonlinear mapping, then a moregeneralized mapping function, rather than a mapping matrix, can be used.

Calculation of the model mapping based on historical data can be done byany suitable training method. An approach similar to a Wiener filter canbe applied, using the following equations:

$\begin{matrix}\begin{matrix}{M = {{{pinv}\left( {X - \overset{\_}{X}} \right)}Y}} \\{= {{pinv}\left\{ {\left( {X - \overset{\_}{X}} \right)^{\prime}\left( {X - \overset{\_}{X}} \right)} \right\} \left( {X - \overset{\_}{X}} \right)^{\prime}Y}} \\{C_{apc} = {\overset{\_}{Y} - {\overset{\_}{X}{M.}}}}\end{matrix} & (5)\end{matrix}$

where piny represents a pseudo-inverse function, and indicates thetranspose of a matrix. The second line in Equation (5) is presented onlyto illustrate the similarity with a Wiener filter. Both the modelmapping matrix M and process corrections C_(apc), can be trained usingoverlay and wafer alignment measurements from the past, for example aspart of a modified APC control loop. The training effectively identifiesthe correlation between wafer alignment and overlay. Use of the modelmapping effectively removes from the substrate model contributions thatwill be corrected through the process model. Over-correction or throughthe mapped substrate model, but over-correction and under-correction ofcorrelated contributions is eliminated.

Subspace Mapping

As mentioned above, dimensionality of the mapped substrate model canalso be reduced, for example by application of known statisticaltechniques. By applying a Singular Value Decomposition to matrix M, forexample, equation (4) can be written as

Y≅XUSV′+C_(apc),   (6)

where U and V are orthogonal coordinate transformation matrices and S isa diagonal matrix containing the singular values of matrix M. Theexpressions XU and YV can in this case be considered as subspaces of theparameter space of X and Y, respectively. Each subspace has dimensionsdefined by a base vector in terms of the parameters of the parameterspace. Each single base vector from XU is mapped onto a single basevector YV with the corresponding singular value from S as a scalingfactor. By deleting selected singular values (setting them to zero), onecan limit the mapping to a linear subspace of the original modelparameter spaces.

Deleting singular values is equivalent to removing columns of thematrices U and V. Note that values in S, XU and YV can be used to selectwhich “subspace” parameters to reject and which to maintain. Forexample, S provides the scaling of the parameter. If the scaling factoris very low (close to 0) this means that the subspace base vector isirrelevant for overlay, and may be discarded. Discarding these termshelps to reduce processing, and leaves the significant contributionsmore visible, if one wants to gain insight into the causes of overlayerror. For example, a pattern of positional deviations that isintroduced by the lithographic apparatus in a current layer, may inpractice be the same as a pattern of deviations introduced by the sameapparatus in exposing a previous layer. This is an example of an errorthat may be present but is irrelevant for overlay and so should not becorrected by the substrate model, even if it appears in the measurementsof the substrate, and could at first sight be corrected in the substratemodel. More significantly, if S provides an (extremely) large singularvalue (scaling factor) in combination with a very weak model parameterin XU, one may want to delete such a base vector. Such a contribution isnot robust or reliable, and could introduce relatively large errors inthe presence of random variations in the input measurements.

With or without subspace mapping, once the model mapping matrix M hasbeen calculated for the historical data, it can be delivered to thelithographic apparatus for use in mapping the substrate model in themanner shown in FIG. 6. Overlay on the current substrates is thusimproved. The model mapping can be delivered for example as part of therecipe data 206 seen in FIG. 3.

As an additional benefit, the method can also improve the correction ofwafer-specific deformations that are not directly correctable in thesubstrate model (due to the restricted degrees of freedom), but arecorrelated with parameters of the substrate model.

Application to Multi-Color Alignment

The modified method can be used to implement improvements that wouldotherwise require specific steps in the control method. As an example,it is known that the response of the alignment sensor AS is different atdifferent wavelengths (colors), and each application requires adifferent color or combination of colors to depending on the particularmaterials and processing of a given substrate. Alignment marks can behard to “see” as they become buried under subsequent product layers.Moreover the marks themselves can become deformed during processing,making the alignment sensor results more color-dependent. One method toaddress this is to use multiple colors in the alignment sensor, and toselect a “best” signal from among the colors, or to use a weightedcombination of colors. An example of such a sensor is described forexample in PCT patent application publication no. WO 2014-146906. Insome embodiments, different polarizations may be used in addition todifferent colors.

As shown in FIG. 7 the model mapping method can be readily adapted toimplement selection and weighting of different color signals. The stepsand components of the method are the same as in FIG. 6, but with fourcolor channels shown in the alignment sensor and substrate model. Thecolor channels are labeled R (red), G (green), NIR (near infrared) andFIR (far infrared). Another alignment sensor might have more channels.Each color channel has its own substrate model SM with a full set ofparameters. Rather than trying separately to determine a best channel touse for a given substrate the training method can simply derive a bestsubstrate model from all the color signals in combination. In anembodiment using singular value decomposition, the color channel thatyields the most reliable position signals will end up with the strongestscaling factors in matrix S. Another channel will have lower scalingfactors, or zero.

As mentioned, another alignment sensor may have channels for differentpolarizations of light, in addition to different colors. In the presentdescription, different colors can be regarded as just one example ofusing different characters of radiation. These different characters canbe defined by their combination of wavelength, polarization,illumination profile or any other parameters that may be found useful todiscriminate the alignment mark in different process conditions.

Further embodiments are provided in below numbered clauses:

-   1. A method of controlling a lithographic apparatus, the method    comprising:-   (a) obtaining historical performance measurements representing    performance of a lithographic process in applying patterns to a    plurality of prior substrates;-   (b) using the historical performance measurements to calculate a    process model relating to the lithographic process;-   (c) after loading a current substrate into a lithographic apparatus,    measuring current positions of a plurality of alignment marks    provided on the current substrate;-   (d) using the measured current positions to calculate a substrate    model relating to the current substrate;-   (e) controlling the lithographic apparatus using the process model    and the substrate model together,-   (f) obtaining historical position measurements obtained at the time    of processing the prior substrates;-   (g) using the historical position measurements and historical    performance measurements together to calculate a model mapping; and-   (h) applying the model mapping to modify the substrate model    calculated in step (d) and using the modified substrate model in    step (e).-   2. A method according to clause 1, wherein the model mapping is a    subspace mapping, mapping from a multidimensional space occupied by    the substrate model to a subspace of a multidimensional space    occupied by the process model.-   3. A method according to clause 2 wherein step (f) further comprises    reducing a dimensionality of the subspace mapping before it is used    in step (g).-   4. A method according to clause 3 wherein reducing the    dimensionality comprises performing a singular value decomposition    of a subspace mapping matrix and modifying certain components in a    scaling matrix of the singular value decomposition.-   5. A method according to clause 4 wherein modifying certain    components of the scaling matrix comprises setting those components    to zero.-   6. A method according to clause 3 wherein reducing the    dimensionality comprises performing at least one of: principal    component analysis, a canonical variate analysis, a canonical    correlation analysis or a discrete empirical interpolation method.-   7. A method according to any of clauses 1 to 6 wherein in step (g)    the historical performance measurements and historical position    measurements are used together with historical correction data    representing corrections that were applied in processing the prior    substrates.-   8. A method according to any of clauses 1 to 7 wherein the substrate    model is calculated with fewer degrees of freedom than the process    model.-   9. A method according to clause 8 wherein the model mapping    expresses the substrate model using the same degrees of freedom as    the process model.-   10. A method according to clause 8 or 9 wherein the degrees of    freedom of the process model are a superset of the degrees of    freedom of the substrate model.-   11. A method according to any of clauses 1 to 10 wherein the process    model comprises an inter-field model and an intra-field model.-   12. A method according to any of clauses 1 to 11 wherein the    substrate model comprises an inter-field model and an intra-field    model.-   13. A control system for a lithographic apparatus, the control    system comprising:    -   storage for historical performance measurements representing        performance of a lithographic process in applying patterns to a        plurality of prior substrates;    -   a process model processor arranged to use the historical        performance measurements to calculate a process model relating        to the lithographic process;    -   a measurement controller for causing measurement of current        positions of a plurality of alignment marks provided on a        current substrate loaded into the lithographic apparatus;    -   a substrate model processor arranged to use the measured current        positions to calculate a substrate model relating to the current        substrate;    -   storage for historical position measurements obtained at the        time of processing the prior substrates;    -   a model mapping processor arranged to use the historical        position measurements and historical performance measurements        together to calculate a model mapping; and-   a patterning controller arranged to control the lithographic    apparatus using the process model and the modified substrate model    together.-   14. A control system according to clause 13, wherein the model    mapping is a subspace mapping, mapping from a multidimensional space    occupied by the substrate model to a subspace of a multidimensional    space occupied by the process model.-   15. A control system according to clause 14 wherein the model    mapping processor is further arranged to reduce a dimensionality of    the subspace mapping before it is used to modify the substrate    model.-   16. A control system according to clause 14 wherein reducing the    dimensionality comprises performing a singular value decomposition    of a subspace mapping matrix and modifying certain components in a    scaling matrix of the singular value decomposition.-   17. A control system according to clause 16 wherein modifying    certain components of the scaling matrix comprises setting those    components to zero.-   18. A control system according to clause 15 wherein reducing the    dimensionality comprises performing at least one of: principal    component analysis, a canonical variate analysis, a canonical    correlation analysis or a discrete empirical interpolation method.-   19. A control system according to any of clauses 13 to 18 wherein to    calculate the model mapping, the historical performance measurements    and historical position measurements are used together with    historical correction data representing corrections that were    applied in processing the prior substrates.-   20. A control system according to any of clauses 13 to 19 wherein    the substrate model is calculated with fewer degrees of freedom than    the process model.-   21. A control system according to clause 20 wherein the model    mapping expresses the substrate model using the same degrees of    freedom as the process model.-   22. A control system according to clause 20 or 21 wherein the    degrees of freedom of the process model are a superset of the    degrees of freedom of the substrate model.-   23. A control system according to any of clauses 13 to 22 wherein    the process model comprises an inter-field model and an intra-field    model.-   24. A control system according to any of clauses 13 to 23 wherein    the substrate model comprises an inter-field model and an    intra-field model.-   25. A method of manufacturing devices wherein device features and    metrology targets are formed on a series of substrates by a    lithographic process, wherein properties of the metrology targets on    one or more processed substrates are measured by a method according    to any of clauses 1 to 12, and wherein the measured properties are    used to adjust parameters of the lithographic process for the    processing of further substrates.-   26. A lithographic apparatus including a measurement system, a    patterning system and a control system, the control system being    according to any of clauses 13 to 24.-   27. A computer program product containing one or more sequences of    machine-readable instructions for implementing the steps of a method    of any of clauses 1 to 12.-   28. A computer program product containing one or more sequences of    machine-readable instructions for causing a processing device or    system of processing devices to implement the control system of any    of clauses 13 to 24.

CONCLUSION

By the techniques disclosed herein, the currently existing methods forcorrecting positional deviations in the received substrates and in thepatterning process can be modified with a model mapping. In this way,the method can better establish the correlation between wafer alignmentand overlay, and avoid systematic over-correction and under-correction.

Both the model mapping and process corrections can be trained togetherusing historic performance data measured on prior substrates afterpatterning and alignment data measured on the prior substrates prior topatterning. The training calculations can be integrated in existingadvanced process control loops, or in a new control system. New hardwareis not required, to achieve improved overlay performance.

Decomposition the model mapping matrix can be applied to bring furtherbenefits. Using a singular value decomposition, for example, a relevantsubspace can be selected. Unnecessary processing can be avoided, whileoptimizing the achieved overlay.

If the substrate model includes model parameters for multiple sensorchannels, for example different alignment colors or different signalprocessing algorithms, the model mapping can also solve problems relatedto process dependency and/or mark deformation. as well, using bothcolor-to-color and shape information properties (“eigenwafers”) of themark deformation.

Information from the model mapping, for example from the singular valuedecomposition, can be analyzed to obtain insights into the nature ofdeformations and overlay errors, and potentially their root causes.

In association with the hardware of the lithographic apparatus and thelithocell LC, an embodiment may include a computer program containingone or more sequences of machine-readable instructions for causing theprocessors of the lithographic manufacturing system to implement methodsof model mapping and control as described above. This computer programmay be executed for example in a separate computer system employed forthe image calculation/control process. Alternatively, the calculationsteps may be wholly or partly performed within a processor a metrologytool, and/or the control unit LACU and/or supervisory control system SCSof FIGS. 1 and 2. There may also be provided a data storage medium(e.g., semiconductor memory, magnetic or optical disk) having such acomputer program stored therein in non-transient form.

Although specific reference may have been made above to the use ofembodiments of the invention in the context of optical lithography, itwill be appreciated that the invention may be used in otherapplications, for example imprint lithography. In imprint lithography,topography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device may be pressed into alayer of resist supplied to the substrate whereupon the resist is curedby applying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured.

The foregoing description of the specific embodiments will so fullyreveal the general nature of the invention that others can, by applyingknowledge within the skill of the art, readily modify and/or adapt forvarious applications such specific embodiments, without undueexperimentation, without departing from the general concept of thepresent invention. Therefore, such adaptations and modifications areintended to be within the meaning and range of equivalents of thedisclosed embodiments, based on the teaching and guidance presentedherein. It is to be understood that the phraseology or terminologyherein is for the purpose of description by example, and not oflimitation, such that the terminology or phraseology of the presentspecification is to be interpreted by the skilled artisan in light ofthe teachings and guidance.

The breadth and scope of the present invention should not be limited byany of the above-described exemplary embodiments, but should be definedonly in accordance with the following claims and their equivalents.

1.-15. (canceled)
 16. A method comprising: obtaining a first value ofeach first parameter of a plurality of first parameters of a model basedon fitting the model to positional data obtained from positionmeasurements across a substrate; modifying, by a hardware computersystem, one or more of the first values based on a characteristic ofoverlay data of a set of previous substrates, wherein the characteristicis associated with the first parameters of the model; and using themodified one or more first values in configuring a lithographicapparatus.
 17. The method of claim 16, wherein the modifying uses amapping operation, wherein the mapping is based on the characteristic.18. The method of claim 17, wherein the mapping is expressed as amatrix.
 19. The method of claim 17, wherein the mapping operation is alinear projection or a nonlinear projection.
 20. The method of claim 16,wherein the first parameters define a model of one or more rotations andone or more magnifications, that at least partially describe a substratedeformation.
 21. The method of claim 16, wherein the first parametersdefine a higher order model at east partially describing a substratedeformation.
 22. The method of claim 21, wherein the higher order modelcomprises at least a 3^(rd) and/or a 5^(th) order polynomial term. 23.The method of claim 16, further comprising obtaining a second value ofeach second parameter of a plurality of second parameters of an overlaycontrol model, wherein the second values are based on the overlay data,24. The method of claim 23, wherein the overlay control model has moredegrees of freedom than the model used in fitting the positional data.25. The method of claim 24, wherein the mapping is further based onextra degrees of freedom of the overlay control model and the use of theextra degrees of freedom in reducing correlation between the model andthe overlay control model.
 26. The method of claim 23, wherein theconfiguring of the lithographic apparatus is further based on one ormore of the second values.
 27. The method of claim 17, furthercomprising using the mapping to modify the model to obtain a modifiedmodel,
 28. The method of claim 27, wherein the mapping is configured toprovide a modified model having less degrees of freedom than the model,29. The method of claim 28, wherein the mapping reduces the number ofone or more insignificant first parameters comprised within the modifiedmodel compared to the number of one or more insignificant firstparameters comprised within the model.
 30. The method of claim 18,further comprising reducing the dimensionality of the matrix.
 31. Themethod of claim 30, wherein the reducing comprises performing a singularvalue decomposition of the matrix.
 32. The method of claim 31, whereinthe positional data is obtained at a plurality of wavelength settings ofthe alignment system.
 33. The method of claim 32, wherein at least awavelength comprised within the plurality of wavelength settings isselected based on a sub-matrix obtained by performing a singular valuedecomposition of the matrix.
 34. A non-transitory computer programproduct containing one or more sequences of machine-readableinstructions therein, the instructions, upon execution by a computersystem, configured to cause the computer system to at least: obtain afirst value of each first parameter of a plurality of first parametersof a model based on fitting the model to positional data obtained fromposition measurements across a substrate: modify one or more of thefirst values based on a characteristic of overlay data of a set ofprevious substrates, wherein the characteristic is associated with thefirst parameters of the model; and use the modified one or more firstvalues in configuring the lithographic apparatus.
 35. A computer system,comprising: a hardware processor system; and the non-transitory computerprogram product of claim 34.